We use "micro-payment channels" such as "Bitcoin Lightning Network" or "Duplex Micro-Payment Channels" for saving transaction fee, accelerating payments, supporting better micro-payment and scaling blockchain.

Is there any difference between "state channel" v.s "micro-payment channel"? and if so, what are differences?

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Payment channels are a specific form of state channels used for forwarding payments (as in the Lightning network). State channels are a more abstract idea: In theory you could use the ideas of cryptographically securing a state between two or more participants (the balance in payment channels) backed by a blockchain for something else than payments (like games). But, just as with blockchains, it is highly doubtful if this actually makes sense economically for anything else than money itself.

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